Deligne–Lusztig duality on the moduli stack of bundles

Chen, Lin

doi:10.1090/ert/645

Deligne–Lusztig duality on the moduli stack of bundles
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by Lin Chen;

Represent. Theory 27 (2023), 608-668

DOI: https://doi.org/10.1090/ert/645

Published electronically: July 24, 2023

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Abstract:

Let $\operatorname {Bun}_{G}(X)$ be the moduli stack of $G$-torsors on a smooth projective curve $X$ for a reductive group $G$. We prove a conjecture made by Drinfeld-Wang and Gaitsgory on the Deligne–Lusztig duality for D-modules on $\operatorname {Bun}_{G}(X)$. This conjecture relates the pseudo-identity functors given by Gaitsgory [Ann. Sci. Éc. Norm. Supér. (4) (2017)] and Drinfeld and Gaitsgory [Camb. J. Math. 3 (2015), pp. 19–125] to the enhanced Eisenstein series and geometric constant term functors given by Gaitsgory [Astérisque (2015)]. We also prove a “second adjointness” result for these enhanced functors.

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